Encoded Message Error Correction Using Selective Polynomial Root Search
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Solution Overview
Problem
Existing error correction algorithms, such as the Bose-Chaudhuri-Hocquenghem (BCH) algorithm, are time-intensive when used in multi-level NAND flash memory due to high error rates and large data blocks, requiring significant time and power to correct even a single bit error.
Innovation Solution
A system and method that employs a search engine to determine error locations by generating syndromes, computing polynomial coefficients, and using a modified Chien search algorithm to solve only relevant solutions, avoiding unnecessary calculations and reducing clock cycles by eliminating the inverting step, thus saving time and power.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional BCH error correction algorithms are used, then error correction capability is achieved, but time consumption and power consumption increase significantly
Solution Approach 1:
The patent segments the error correction process into distinct functional modules: syndrome computation unit, root finding unit, and error location determination unit. This segmentation allows each unit to be optimized independently and enables parallel processing of multiple operations, significantly reducing the overall time consumption while maintaining complete error correction capability
Solution Approach 2:
The patent performs preliminary computation of polynomial coefficients and syndrome values before the actual error correction is needed. By pre-computing these values and storing them in lookup tables, the system eliminates time-consuming calculations during the error correction process itself, reducing real-time processing time while preserving full error correction functionality
2Reliability
If traditional BCH error correction algorithms are used, then error correction capability is achieved, but power consumption increases significantly
Solution Approach 1:
By dividing the error correction circuit into segmented functional units that can operate independently and in parallel, the patent reduces the simultaneous activation of circuit components. This segmentation lowers peak power consumption while maintaining the ability to correct errors, as not all circuit elements need to be active at the same time
Solution Approach 2:
The patent employs lookup tables with pre-computed values that can be quickly referenced and then discarded. This approach replaces complex, power-intensive calculation circuits with simpler, lower-power lookup operations. The lookup tables are regenerated periodically but are not continuously updated, reducing the average power consumption while maintaining error correction capability
3Measurement precision
If complete polynomial equation solutions are computed, then all potential error locations are identified, but unnecessary calculations increase time consumption
Solution Approach 1:
The patent extracts only the relevant roots of the polynomial equation that correspond to actual error locations in the code word. By using the syndrome values to directly identify which roots are relevant and applying efficient root-finding algorithms, the system determines error locations without computing all possible polynomial solutions, thereby reducing calculation time while maintaining precise error location identification
Solution Approach 2:
The patent applies partial action by computing only the necessary portion of the polynomial solutions needed to correct the actual number of errors present. Instead of exhaustively solving for all potential error locations regardless of actual error count, the system adapts the computation to match the actual error situation, reducing unnecessary calculations while ensuring all real errors are located with high precision
Data Source
AI summary
An encoded message is stored in a first memory. The encoded message is retrieved from the first memory as a retrieved encoded message that may contain an error. Syndromes are generated from the retrieved encoded message. The syndromes are used to determine if the retrieved encoded message has an error. Polynomial coefficients are generated for establishing a polynomial equation having a first number of solutions. The polynomial equation is solved only for a second number of solutions. The first number is greater than the second number. The second number of solutions comprises solutions corresponding to locations in the retrieved encoded message. Each location is corrected in the retrieved encoded message that corresponds to a solution of zero of the polynomial equation. The result is efficient error correction.